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Ijraset Journal For Research in Applied Science and Engineering Technology

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Integral Solutions of the Ternion Quadratic Equation

Authors: Gowri Shankari A, Sangavi S

DOI Link: https://doi.org/10.22214/ijraset.2023.49490

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Abstract

In order to find its non zero unique integral solutions for the quadratic diophantine equation with three unknowns given by is analysed. The equation under consideration exhibits multiple patterns of solutions. The solutions are presented with a few fascinating aspects.

Introduction

Conclusion

For the ternion quadratic equation we have given numerous non-zero unique integral solutions patterns. To conclude, one can look for further options for solutions and their respective attributes among the various choices.

References

[1] Carmichael R.D., “The Theory of Numbers and Diophantine Analysis”, Dover Publications, New York, 1959 [2] Dickson L.E., “History of the theory of numbers”, Chelsia Publishing Co., Vol II, New York, 1952 [3] Telang S. G., “Number Theory”, Tata Mc Graw-Hill Publishing Company, New Delhi 1996 [4] Mordell L.J., “Diophantine Equations”, Academic Press, London 1969 [5] Janaki G, Gowri Shankari A, “Properties of the Ternary Cubic Equation ”, International Journal for Research in Applied Science and Engineering Technology, Vol 10, Issue VIII,Pg.No: 231-234, August 2022 [6] Janaki G, Saranya C, “Observations on Ternary Quadratic Diophantine Equation ”, International Journal of Innovative Research and science, Engineering and Technology, Volume 5, Issue 2, February 2016 [7] Devibala. S, Gopalan M.A, “On the ternary quadratic Diophantine equation ”, International Journal of Emerging Technologies in Engineering Research, 4(9), 2016, 6-7. [8] Gopalan M.A, Vidhyalakshmi. S and Aarthy Thangam. S, “On the ternary quadratic equation ”, Vol-6, Issue-8, August 2017. [9] Gopalan M.A, Vidhyalakshmi. S and Rajalakshmi. U.K, “On the ternary quadratic diophantine equation ”, Vol-3, Issue-5, May 2017, 1-10. [10] Janaki G, Radha R, “On ternary quadratic diophantine equation ”, International Journal for Research in Applied Science and Engineering Technology”, Vol 6, Issue I, Pg. No: 2656-2660, January 2018 [11] Gopalan M.A, Vidhyalakshmi. S and Nivetha. S,”On the ternary quadratic equation ” Diophantus J. Math, 3(1), 2014, 1-7. [12] Gopalan M.A, Vidhyalakshmi. S, “On the ternary quadratic diophantine equation ”, BOMSR, Vol 2, No.4,2014, 429-433. [13] Gopalan M.A, Vidhyalakshmi. S and Usha Rani T.R, “Integral points on the non-homogeneous one ”, Global journal of Mathematics and Mathematical Science, 2(1),2012, 61-67. [14] Gopalan M.A, Vidhyalakshmi. S and Usha Rani T.R, “On the ternary quadratic Diophantine equation “, Sch.J.Eng Tech., 2(2A),2104,108-112 [15] Janaki. G, Vidhya. S On the integer solutions of the homogeneous biquadratic diophantine equation , International Journal of engineering Science and Computing 6(6) (2016), 227-229.

Copyright

Copyright © 2023 Gowri Shankari A, Sangavi S. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Paper Id : IJRASET49490

Publish Date : 2023-03-11

ISSN : 2321-9653

Publisher Name : IJRASET

DOI Link : Click Here